Hank's teacher asked him to verify that the product (y - 3) (y2 + 3y + 9) is a difference of cubes. He used the distributive property to multiply the binomial times the trinomial. Before simplifying, his product was a polynomial of the form y3 + 3y2 + ay - 3y2 - ay - 27. What is the value of a in the polynomial?

Question

Mathematics

Sincere

4 January, 07:38

Hank's teacher asked him to verify that the product (y - 3) (y2 + 3y + 9) is a difference of cubes. He used the distributive property to multiply the binomial times the trinomial. Before simplifying, his product was a polynomial of the form y3 + 3y2 + ay - 3y2 - ay - 27. What is the value of a in the polynomial?

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Clara Johnson · Answer 1

When using the distributive property you have to multiply each term in the parenthesis by each term in the other parenthesis. In this case, you have to multiply y by every term in y2 + 3y + 0 and then multiply - 3 by every term in y2 + 3y + 0. Using the distributive property for the equation we get y3 + 3y2 + 9y - 3y2 - 9y - 27. Looking at this equation, we get a to be 9.